The Mechanics of Looped Arches with Non-parallel or Angulated Legs

1987 ◽  
Vol 14 (3) ◽  
pp. 161-167 ◽  
Author(s):  
N. E. Waters ◽  
P.J. Ward
Keyword(s):  
Radial Displacement ◽  
Beam Theory ◽  
Good Agreement

The force-deflection characteristics, of two unusual types of multiple loop arch, to vertical and radial displacement, are derived from simple beam theory. Check measurements on enlarged models were in good agreement with the theory presented. The variations in stiffness resulting from changes in the size, shape and geometry of the loops is discussed, and the results compared with behaviour of standard vertical loops.

scholarly journals Bi-Dimensional Deflection Estimation by Embedded Fiber Bragg Gratings Sensors

Proceedings ◽  
2019 ◽  
Vol 15 (1) ◽  
pp. 3
Author(s):  
Palma ◽  
Palumbo ◽  
Pietra ◽  
Canale ◽  
Alviggi ◽  
...  
Keyword(s):  
Real Time ◽  
Fiber Bragg Gratings ◽  
Beam Theory ◽  
Bragg Gratings ◽  
Strain Sensors ◽  
Structural Monitoring ◽  
Direct Measure ◽  
Large Structure ◽  
Good Agreement ◽  
Classical Beam Theory

In this work, we present and discuss on the deflection estimation of a bi-dimensional panel by using Fiber Bragg Gratings (FBGs) as strain sensors embedded in the structure and a method based on the classical beam theory. The existing difficulties in the direct measure of the deflection are overcome thanks to the proposed technique and a real-time indirect structural monitoring is possible both on small and large structure. In many tests the estimated deflection with the proposed method has been compared with direct deflection measurements obtained with a mechanical comparator showing good agreement. A resolution of few tens of microns over a surface of the order of 1 m2 has been reached.

scholarly journals Influence of Frequency on the Resolution of Magnetostrictive Bio-Inspired Whisker Sensors

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ran Zhao ◽  
Bo-wen Wang ◽  
Quan-guo Lu ◽  
Jian-wu Yan ◽  
Xiao-cui Yuan
Keyword(s):  
Vibration Frequency ◽  
Dynamic Testing ◽  
Theoretical Calculations ◽  
Beam Theory ◽  
Experimental System ◽  
Flow Sensors ◽  
Maximum Resolution ◽  
Sensing Model ◽  
Euler Bernoulli Beam ◽  
Good Agreement

Magnetostrictive biomimetic whiskers have been used as tactile and flow sensors. Compared to other types of whiskers, such whiskers have the advantage of being able to perform static and dynamic measurements. For dynamic measurement, the whisker’s resolution changes with varying vibration frequency; however, the mechanism for this influence has not been studied yet. Thus, the aim of this study is to investigate the resolution–frequency correlation. First, the structure and operation principle of the whisker were analyzed. Then, the Euler–Bernoulli beam theory was employed to establish the sensing model of the magnetostrictive whisker. Finally, the mapping relationship between sensor resolution and frequency was obtained. The eigenfrequency analysis was implemented by FEM to obtain the frequency response of the whisker. A vibration experimental system was built for dynamic testing. The experimental results were in good agreement with the theoretical calculations. Furthermore, it was noted that the resolution was positively correlated with frequency, and the maximum resolution was attained at the natural frequency (two peak values appeared at the first-order and second-order eigenfrequencies). Our research reveals the manner in which a whisker sensor’s resolution is affected by the vibration frequency. The theoretical model can be used to predict the resolution of magnetostrictive whisker sensors.

Free Vibration of Curvilinearly Stiffened Shallow Shells

2013 ◽  
Author(s):  
Peng Shi ◽  
Rakesh K. Kapania
Keyword(s):  
Free Vibration ◽  
Ritz Method ◽  
Beam Theory ◽  
Fe Method ◽  
Shallow Shells ◽  
First Order ◽  
Stiffened Shells ◽  
Method Base ◽  
Doubly Curved ◽  
Good Agreement

The free vibration of curvilinearly stiffened doubly curved shallow shells is investigated by the Ritz method. Base on the first order shear deformation shell theory and Timoshenko’s 3-D curved beam theory, the strain and kinetic energies of the stiffened shells are introduced. Numerical results with different geometrical shells and boundary conditions, and different stiffener locations and curvatures are analyzed to verify the feasibility of the presented Ritz method for solving the problems. The results show good agreement with those using the FE method.

Electrothermally Tunable Bridge Resonator

2016 ◽  
Author(s):  
Amal Z. Hajjaj ◽  
Nouha Alcheikh ◽  
Abdallah Ramini ◽  
Md Abdullah Al Hafiz ◽  
Mohammad I. Younis
Keyword(s):  
Fundamental Frequency ◽  
Beam Theory ◽  
Element Model ◽  
Bernoulli Beam ◽  
Electrothermal Actuation ◽  
Wide Range ◽  
Simulation Results ◽  
Dc Current ◽  
Euler Bernoulli Beam ◽  
Good Agreement

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of an in-plane clamped-clamped microbeam, bridge, and resonator compressed by a force due to electrothermal actuation. We demonstrate that a single resonator can be operated at a wide range of frequencies. The microbeam is actuated electrothermally, by passing a DC current through it. We show that when increasing the electrothermal voltage, the compressive stress inside the microbeam increases, which leads eventually to its buckling. Before buckling, the fundamental frequency decreases until it drops to very low values, almost to zero. After buckling, the fundamental frequency increases, which is shown to be as high as twice the original resonance frequency. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and to simulation results of a multi-physics finite-element model. A good agreement is found among all the results.

Vibration Analysis of Multi-Cracked Beam Traversed by Moving Masses Using Discrete Element Technique

2013 ◽  
Vol 376 ◽  
pp. 220-223
Author(s):  
Reza Alebrahim ◽  
Nik Abdullah Nik Mohamed ◽  
Sallehuddin Mohamed Haris ◽  
Salvinder Singh Karam Singh
Keyword(s):  
Vibration Analysis ◽  
Beam Theory ◽  
Discrete Element ◽  
Maximum Deflection ◽  
Bernoulli Beam ◽  
Cracked Beam ◽  
Time To Build ◽  
Element Technique ◽  
Euler Bernoulli Beam ◽  
Good Agreement

The vibration analysis of a multi-cracked beam using discrete element technique (DET) was investigated in this study. Undamped simply supported beam was traversed by moving mass with constant speed and Euler Bernoulli beam theory was considered. Cracks are located in different positions and maximum deflection of mid-span was derived and compared. The results showed that increasing numbers of cracks in the beam causes more deflection while maximum deflection of beam takes longer time to build up. The results were validated by solving the equations generated using finite element method (FEM) and their comparison with already established results from previous similar studies (literatures) showed good agreement.

Dynamic Analysis of Tapered Plates Based on Higher Order Beam Theory

2014 ◽  
Vol 919-921 ◽  
pp. 79-82
Author(s):  
S.M. Ibrahim ◽  
Y.A. Al-Salloum ◽  
H. Abbas
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Beam Theory ◽  
Longitudinal Axis ◽  
Vibration Modes ◽  
Bending Vibration ◽  
3D Finite Element ◽  
Different Types ◽  
Tapered Plates ◽  
Good Agreement

Modal solutions of plates with uniformly varying cross section using unified beam theory are presented. The results are given in the form of Euler-Bernoulli, Timoshenko and quasi 3D solutions. Numerical results for cantilever and CFCF supported rectangular planform plates are presented. Different types of modes, i.e. axial, bending and torsional modes are observed. The frequency values are in good agreement with 3D finite element results as well as published literature. Due to uniform taper in plate cross section, bending vibration modes become asymmetric along the longitudinal axis of the structure. Further, it can also be noticed that the vibration behavior of thick tapered plates is characterized by the appearance of significant number of axial and torsional modes at lower frequency values.

scholarly journals The Effect of Transverse Shear in Symmetric and Asymmetric End Notch Flexure Tests–Analytical and Numerical Modeling

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3046
Author(s):  
Konrad Dadej ◽  
Paolo Sebastiano Valvo ◽  
Jarosław Bieniaś
Keyword(s):  
Transverse Shear ◽  
Beam Theory ◽  
Bending Moment ◽  
Pure Mode ◽  
Planar Shear ◽  
Transverse Shearing ◽  
Numerical Finite Element ◽  
Rigid Interface ◽  
Moment State ◽  
Good Agreement

This paper focuses on the effects of transverse shear and root rotations in both symmetric and asymmetrical end-notched flexure (AENF) interlaminar fracture toughness tests. A theoretical model is developed, whereas the test specimen is subdivided into four regions joined by a rigid interface. The differential equations for the deflection and rotations of each region are solved within both the Euler–Bernoulli simple beam theory (SBT) and the more refined Timoshenko beam theory (TBT). A concise analytical equation is derived for the AENF deflection profile, compliance, and transverse shearing forces as a function of the specimen geometry, stacking sequence, delamination length, and fixture span. Modeling results are compared with numerical finite element analyses, obtaining a very good agreement. Performed analyses suggest that even in the case of symmetrical and unidirectional laminates considered as pure mode II fracture, a complex compression/tension and bending moment state is present, as well as a slight contribution of anti-planar shear at the vicinity of the crack tip.

A Homogenization Procedure for Nonlinear Free Vibration Analysis of Functionally Graded Beams Resting on Nonlinear Elastic Foundations

2012 ◽  
Vol 232 ◽  
pp. 427-431
Author(s):  
Ahmed Zerkane ◽  
Khalid El Bikri ◽  
Rhali Benamar
Keyword(s):  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Axial Stiffness ◽  
Nonlinear Frequency ◽  
Homogenization Procedure ◽  
Nonlinear Elastic ◽  
Good Agreement

The present work deals with a homogenization procedure (HP), which is developed to reduce the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) resting on elastic nonlinear foundation with immovable ends to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results.

Synthesis, Characterization and Analytical Modelling of Mechanical Behavior of a Conducting Polymer Actuator

2010 ◽  
Vol 654-656 ◽  
pp. 2467-2470 ◽  
Author(s):  
Akif Kaynak ◽  
Chun Hui Yang ◽  
Abbas Kouzani
Keyword(s):  
Propylene Carbonate ◽  
Operating Time ◽  
Beam Theory ◽  
Pvdf Film ◽  
Layer Model ◽  
Triple Layer ◽  
Conductive Film ◽  
Pyrrole Monomer ◽  
Polymer Actuator ◽  
Good Agreement

Electrochemical synthesis of a tri-layer polypyrrole based actuator optimized for performance was reported. The 0.05 M pyrrole and 0.05 M tetrabutylammonium hexaflurophosphate in propylene carbonate (PC) yielded the optimum performance and stability. The force produced ranged from 0.2 to 0.4mN. Cyclic deflection tests on PC based actuators for 3 hours indicated that the displacement decreased by 60%. PC based actuator had a longer operating time, exceeding 3 hours, compared to acetonitrile based actuators. A triple-layer model of the polymer actuator was developed based on the classic bending beam theory by considering strain electrode material. A tri-layer actuator was fabricated [4, 6], by initially sputter coating a PVDF film with approximately 100nm of gold layer, resulting in a conductive film with a surface resistance of 8-10Ω. The PVDF film was about ~145µm thick had an approximate pore size of 45μm. A solution containing 0.05M distilled pyrrole monomer, 0.05M (TBAPF6) and 1% (w/w) distilled water in PC (propylene carbonate) solution was purged with nitrogen for 15 minutes. The continuity between PPy and PVDF. Results predicted by the model were in good agreement with the experimental data.

The Effect of Chucking Methods on Roundness Error in the Boring Process

1976 ◽  
Vol 98 (1) ◽  
pp. 233-238 ◽  
Author(s):  
C. H. Kahng ◽  
H. W. Lord ◽  
T. L. Davis
Keyword(s):  
Theoretical Model ◽  
Beam Theory ◽  
Geometric Parameters ◽  
Curved Beam ◽  
Roundness Error ◽  
Cylindrical Workpiece ◽  
Analytical Expressions ◽  
Good Agreement

Curved-beam theory is used to obtain a theoretical model to describe deformations in a cylindrical workpiece during boring processes. Analytical expressions are obtained for roundness error due to two-, three-, and four-jaw chucks. Experiments are carried out and theory is compared with measured values of roundness errors for several combinations of material and geometric parameters, showing good agreement.

Sign in / Sign up

Export Citation Format

Share Document